Solve for $a$, $ \dfrac{3}{16a + 16} = -\dfrac{3}{4a + 4} - \dfrac{4a - 5}{12a + 12} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $16a + 16$ $4a + 4$ and $12a + 12$ The common denominator is $48a + 48$ To get $48a + 48$ in the denominator of the first term, multiply it by $\frac{3}{3}$ $ \dfrac{3}{16a + 16} \times \dfrac{3}{3} = \dfrac{9}{48a + 48} $ To get $48a + 48$ in the denominator of the second term, multiply it by $\frac{12}{12}$ $ -\dfrac{3}{4a + 4} \times \dfrac{12}{12} = -\dfrac{36}{48a + 48} $ To get $48a + 48$ in the denominator of the third term, multiply it by $\frac{4}{4}$ $ -\dfrac{4a - 5}{12a + 12} \times \dfrac{4}{4} = -\dfrac{16a - 20}{48a + 48} $ This give us: $ \dfrac{9}{48a + 48} = -\dfrac{36}{48a + 48} - \dfrac{16a - 20}{48a + 48} $ If we multiply both sides of the equation by $48a + 48$ , we get: $ 9 = -36 - 16a + 20$ $ 9 = -16a - 16$ $ 25 = -16a $ $ a = -\dfrac{25}{16}$